The obvious answer is yes, basically any time there is damage of these or other structures during an earthquake (of which there are of course numerous examples), ultimately the root cause is plate movement as this is driving the storage of elastic energy that is released during an earthquake.

That being said, I assume you're more asking about whether slow and steady motion along plate boundaries can damage infrastructure. This depends a bit on the nature of the faults in question. For those that fail seismically (i.e., with earthquakes) the answer would generally be no. During the interseismic period, i.e., the time between earthquakes, while strain is accumulating, this deformation is distributed over long enough distances that the differential rate of motion over even "long" features like bridges, etc., will be very small and generally less than things like thermal expansion which are accounted for in the design of most of these structures.

However, there are "creeping" faults, or creeping sections of faults, i.e., portion of faults that experience slow and steady "creep" near the slip-rate of the fault as opposed to accumulating strain to be released during an earthquake. If a structure spans a creeping fault, it will gradually be displaced. Classic examples of this can be found along several creeping faults that go through cities, probably one of the more famous being the Hayward fault that goes through Berkeley, CA. Within Berkeley, along the fault, there are a variety of structures like curbs and even large sections of the Cal football stadium - scroll down to page 13 and after that are offset by creeping motion of the Hayward. Specific to bridges, probably one of the most famous examples of fault creep deforming a bridge is a bridge near Parkfield, CA being deformed by creep along the San Andreas fault.

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